Resonance Raman Scattering of Light from a Diatomic Molecule

University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Electrical & Computer Engineering, Department P. F. (Paul Frazer) Williams Publications of May 1976 Resonance Raman scattering of light from a diatomic molecule D. L. Rousseau Bell Laboratories, Murray Hill, New Jersey P. F. Williams University of Nebraska - Lincoln, [email protected] Follow this and additional works at: https://digitalcommons.unl.edu/elecengwilliams Part of the Electrical and Computer Engineering Commons Rousseau, D. L. and Williams, P. F., "Resonance Raman scattering of light from a diatomic molecule" (1976). P. F. (Paul Frazer) Williams Publications. 24. https://digitalcommons.unl.edu/elecengwilliams/24 This Article is brought to you for free and open access by the Electrical & Computer Engineering, Department of at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in P. F. (Paul Frazer) Williams Publications by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Resonance Raman scattering of light from a diatomic molecule D. L. Rousseau Bell Laboratories. Murray Hill, New Jersey 07974 P. F. Williams Bell Laboratories, Murray Hill, New Jersey 07974 and Department of Physics, University of Puerto Rico, Rio Piedras, Puerto Rico 00931 (Received 13 October 1975) Resonance Raman scattering from a homonuclear diatomic molecule is considered in detail. For convenience, the scattering may be classified into three excitation frequency regions-off-resonance Raman scattering for inciderit energies well away from resonance with any allowed transitions, discrete resonance Raman scattering for excitation near or in resonance with discrete transitions, and continuum resonance Raman scattering for excitation resonant with continuum transitions, e.g., excitation above a dissociation limit or into a repulsive electronic state. It is shown that the many differences in scattering properties in these three excitation frequency regions may be accounted for by expressions derived from simple perturbation theory. Scattering experiments from molecular iodine are presented which test and verify the general scattering theories. Spectral measurements, time decay measurements, and pressure broadening measurements were made on I, in the discrete resonance Raman scattering region; and spectral measurements at several excitation frequencies were made in the continuum resonance Raman scattering region. In each cace calculations based on general theories correctly describe the experimental data. I. INTRODUCTION behavior in these three regions is so great that they have been used to classify1 the re-emission into normal Over the past few years a great deal of interest has Raman scattering, resonance fluorescence, and reso- developed in the understanding of resonance Raman nance Raman scattering, respectively. This empirical scattering and its application to problems in chemistry, physics, and biology. Most of these studies have been classification, resulting from the marked differences in the scattering behavior, have led to a popular belief2 devoted to either solids or complex biological mole- that fundamental theoretical differences exist between cules, and relatively little attention has been given to Raman scattering, resonance Raman scattering, and simple gaseous molecules. Resonance Raman scat- resonance fluorescence. As pointed out recently by tering is generally not well understood, and the work on Behringer, 3*4 this problem is not new, but dates back solids and complex molecules has done little to clarify to the turn of the century with the question of the dif- the basic mechanisms. In solids, the lack of success ferences between ordinary Rayleigh scattering and may be attributed to complicated electronic structures, resonance Rayleigh scattering. Since this time, two impurities, anisotropies, and ill defined electron- schools of thought have evolved concerning the origins phonon interactions. Similarly, biological molecules of resonance and nonresonance scattering. The first often have strong complex absorption bands; vibrational asserts that the long-lived resonance fluorescence pro- modes may not be readily assigned; broad fluorescence cess is a different physical process than short-lived frequently obscures the discrete structure; and the resonance scattering. The distinction between spectra have a marked excitation frequency dependence. am an the processes is made by asserting that in resonance In contrast, the electronic structure of some small fluorescence the excitation and re-emission may be molecules are quite simple and very well known. divided into a real absorption followed independently by Therefore, the properties of the light scattering from a real emission. In contrast, it is argued that in Ra- such molecules as the incident laser frequency is man scattering (or Rayleigh scattering) this bisection varied from nonresonance, to resonance with discrete of the elementary processes is impossible. It is con- vibration-rotation levels of an excited state, and then sequently concluded that two distinguishably different at high laser energies to resonance with continuum physical processes account for these phenomena. The states, should serve to elucidate the nature of the other viewpoint is that resonance fluorescence and Ra- fundamental processes. In this paper we discuss the scattering behavior of monochromatic light when the man scattering, including resonance Raman scattering, intermediate states are isolated discrete vibrational- are all one process with the empirical differences in- rotational levels of a diatomic molecule and the scat- terpretable from the excitation frequency differences tering behavior when the intermediate states belong to alone. a continuum. Consideration of the scattering of monochromatic Empirically, very different scattering spectra are light from simple gaseous diatomic molecules clarifies obtained if the incident laser frequency is far from this question in a definitive way. As long as scattering resonance, is in resonance with transitions to discrete amplitudes from nearby states are sufficiently small, states, or is in resonance with transitions to con- compared to the resonant state under consideration, so tinuum states. The differences between the scattering as to be neglected, and as long as quasielastic collision- The Journal of Chemical Physics, Vol. 64, No. 9, 1 May 1976 Copyright O 1976 American Institute of Physics 3519 D. L. Rousseau and P. F. Williams: Resonance Rarnan scattering FIG. 1. Classification of Raman scattering according to laser frequency. A. The incident laser frequency is far from resonance with any real electronic transition, so normal Raman scattering is' observed. B. The incident laser frequency is in the region of discrete levels of a single electronic intermediate state. We term this process discrete reso- w nance Raman scattering. C. The incident frequency is in B C the range of a dissociative DISCRETE CONTINUUM continuum. We label this RESONANCE RESONANCE process continuum resonance Raman scattering;.. RAMAN RAMAN RAMAN SCATTERING SCATTERING SCATTERING a1 broadening effects are small, no distinction between Ranzan scattering. In the center, when the incident resonance fluorescence and resonance Raman scatter- frequency is in the region of discrete vibronic transi- ing may be made. From perturbation theory a general tions we term the re-emission discrete resonance expression may be derived which is valid for scatter- Raman scattering independent of whether or not the ing of monochromatic light independent of the excita- incident frequency is at exact resonance. To the right, tion frequency. The spectrum of scattered light obeys when the incident frequency is above the excited state this simple formalism and varies in a predictable sys- dissociation limit in a continuum region, we label the tematic way with excitation frequency. From the theory re-emission as continuum resonance Raman scattering. it is clear that even for exact resonance the excitation To illustrate the general light scattering principles and the re-emission process are not independent, be- discussed in this paper we have selected molecular cause the emitted photon retains the phase information iodine as an example. I, was chosenfor the experiments of the excitation step. because it is nearly ideally suited both experimentally At exact resonance, the scattering amplitude diverges and theoretically. First, iodine's electronic structure owing to the pole in the denominator, and a damping and the energies of the vibrational-rotational levels are term must be included. If we take the relevant matrix very well known6 from fluorescence, predissociation, elements to be real, then doing so introduces an imag- and photofragmentation experiments. Secondly, io- inary component into the scattering amplitude which is dine is a single isotope, homonuclear diatomic mole- strongly peaked at this resonant frequency. It then be- cule with only a single vibrational degree of freedom. comes tempting to classify the real part as resonance Finally, as illustrated in Fig. 2, the presence of an Raman scattering and the imaginary part as resonance excited electronic state with a dissociation limit at 20, fluorescence. This arbitrary separation into ill-de- 162 cm-I above the bottom of the ground state well, fined processes is confusing, however, since each term makes it possible to investigate resonance processes results from the same perturbation expression. The below

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